Closeness of Performance Map Information Granules: A Rough Set Approach

Abstract

This article introduces a rough set approach to measuring of information granules derived from performance maps. A performance map employs intuitive color-coding to visualize the behavior of system dynamics resulting from variations in system parameters. The resulting image is developed algorithmically via digital computation. With only moderate á priori knowledge, mathematical analysis of a performance map provides an immediate wealth of information. This study is motivated by an interest in measuring the separation between “islands” (collections of pixels with the same color) representing normal (e.g., black pixels) and potentially chaotic (e.g., red pixels) system behavior. A performance map island or sector is identified with groupings of cells in a mesh resulting from the partition of a performance map into equivalence classes. The information granules considered in this paper are associated with a feature set in an information system. The contribution of this article is the application of a measures of granule closeness based on an indistinguishability relation that partitions performance maps intervals into sub intervals (equivalence classes). Such partitions are useful in measuring closeness of map cells containing color-coded pixels used to visualize dynamical system behavior.